SaxMarc:
I'm doing exactly what you're planning to do, except I'm on guitar with vocals. All the suggestions provided are excellent for that type environment. I'd recommend the American songbook variety, with a sprinking of easy country and pop tunes through about the 70's and 80's. Include a few movie and TV sitcom themes as well. I even get away with the western swing thing, since that's one of my favorite styles. My gig is the white table cloth routine in a university town with private membership. BIAB works great for the solo artist. I have guest vocalists and instrumentalists who often join me and they all can't say enough good stuff about BIAB. So far it's never failed on a gig. If that happened, I'd pull-out the mp3 player.